To get the Short Controlled Bursts achievement in State of Decay 2 do the following:
You max out skills by putting them to use. Shoot enough with a character and they'll eventually max out the first-tier shooting skill and you'll be able to choose a specialization on top of your previous bonuses.
Access that menu by pressing down on the D-Pad, then LB to look at your skills. Pick one of the two seemingly randomized specialization skills and the achievement is yours.
Edit: As commenters have pointed out below, this achievement may only pop if the skill you're upgrading belongs to your active character, so be sure to have that character in use at the time of your skill acquisition.